Stabilizing region of fractional-order proportional integral derivative controllers for interval fractional-order plants

Abstract

This paper focuses on computing the stabilizing region of fractional-order proportional integral derivative (FOPID) controllers for interval fractional-order plants. In this study, first, a theorem is presented to investigate the robust stability of the given closed-loop system. Then, an algorithm is proposed to solve the problem of robustly stabilizing the interval fractional-order plant using FOPID controllers. Also, two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction. Finally, four numerical examples are presented to confirm the obtained results.